main.py

def get_second_area_moment(breadth, depth):
    return breadth * depth**3/12


def get_natural_frequency(youngs_modulus, sam, mass, length, eigenvalue):
    return eigenvalue * ((youngs_modulus * sam)/(mass * length**4))**(1/2)


def get_light_beam_stiffness(length, youngs, sam):
    return (3 * youngs * sam)/(length**3)


def get_natural_frequency_massless_spring(mass, stiffness):
    return (stiffness/mass)**(1/2)


def get_natural_frequency_real_beam(youngs, sam, length):
    return ((140 * youngs * length)/(11 * length**4))**(1/2)


# INPUT
GRAVITATIONAL_ACCELERATION = 9.81
LENGTH = 350e-3
BREADTH = 25e-3
YOUNGS_MODULUS = 200e9
DEPTH = 3e-3
VOLUME = LENGTH * BREADTH * DEPTH
BEAM_DENCITY = 7850
MASS_NOMINAL = BEAM_DENCITY * VOLUME
MASS_TOTAL = 118e-3
MASS_EXTRA = MASS_TOTAL - MASS_NOMINAL
BEAM_MASS_PER_LENGTH = MASS_NOMINAL / LENGTH

print("volume", VOLUME)
print("beam length", LENGTH)
print("beam mass", MASS_NOMINAL)
print("beam mass per length", BEAM_MASS_PER_LENGTH)
sam = get_second_area_moment(BREADTH, DEPTH)
print("cross sectional area moment", sam)

EIGENVALUE = 3.516


masses = [0.118, 0.418, 0.618]
# TODO: light beam and real beam
for mass in masses:
    # natural_frequency = get_natural_frequency(YOUNGS_MODULUS, sam, mass, LENGTH, EIGENVALUE)
    # print("mass, natural frequency", mass, natural_frequency)
    stiffness = get_light_beam_stiffness(LENGTH, YOUNGS_MODULUS, sam)
    # print("mass, stiffness", mass, stiffness)
    natural_frequency = get_natural_frequency_massless_spring(mass, stiffness)
    natural_period = natural_frequency**(-1)
    print("mass, natural frequency, natural period", mass, natural_frequency, natural_period)
    real_natural_frequency = get_natural_frequency_real_beam(YOUNGS_MODULUS, sam, LENGTH)
    print("real natual period", real_natural_frequency ** (-1))